## Triangular Peg/Marble Solitaire Instructions

Jump one peg over another into an empty spot, removing the jumped peg from the board. You can jump along any of the three directions parallel to the outside edges of the board. Just click on a peg and if there's a jump available, the peg will jump. If there's more than one jump available, you'll need to click on a destination. The goal is to finish with one peg.

### What is "Never Lose"?

If you move your mouse over a peg (without clicking), and it turns into a bomb, this indicates that moving this peg leads to a dead end. You will also run into the situation where a peg has several possible jumps, some good and some bad. In this case the peg will not turn to a bomb, but the bad landing site(s) will be marked by a black X, and the good landing site(s) will be marked by a red X. Note that "leads to a dead end" means that you won't be able to finish with one peg, either at the board location originally vacant or anywhere on the board, depending on how the Assistance control below is set. Remember, in this puzzle,
 red is good, black is bad

 If you want to always win, avoid clicking on a bomb! Never click on a bomb, and never move a peg to a destination hole with a black X (if you do so by mistake, hit the "Back" button to take the move back). Then, hunt around with your mouse for a red peg or a red X (there will always be at least one, if you never make a bad move). Now you will win every time!

### What do all the controls do?

 Resets the game to the starting position with one peg missing. Fills the entire board with pegs. Click on one of them to set the starting vacancy (peg missing at the start). Then begin play as usual, or hit Solve. Take back the last jump (all the way back the start if you like). Very useful if you reach a dead end. You can also take back moves made in solve mode. Solve the puzzle from the current board position down to one peg ("solve mode"). This final peg can be forced to end at the starting position, as selected by the Assistance control. The board is solved by selecting a random (good) jump, so if you repeat this command you will likely get a different solution (unlike the Ultimate Version where the solution is always the same). When in solve mode, this button changes to Pause, and if you click it the solving will pause, and the button changes to Continue. You can use these controls to halt at any intermediate point. Change the board (10, 12, 15, 18 or 21 holes). This sets the time delay between jumps when the Solve button has been selected. You can even change this control while a solution is playing, to speed it up or slow it down. Slow, Normal, Fast, Faster and Fastest correspond to delays of 2, 1, 1/2, 1/10 and 0 seconds between jumps. This changes the settings for when those helpful bombs appear. You can even change this setting in the middle of the game, but not in solve mode. "I don't need any help" means no bombs will ever appear. The Solve button won't work when this option is selected. "Finish where I started" means that a bomb will appear on any dead end where it is impossible to finish at the hole that was originally empty. On the 15-hole board, if you start in the interior, it is impossible to finish where you started, so you will see only bombs for the first jump. "Finish anywhere" means that a bomb will appear on any dead end where it is impossible to play to one peg. This setting allows for the greatest number of possible jumps.

### What's that weird text that appears during a solution?

The program records the move sequence in a format that looks like this:

 6 moves: e5-c5, b5-d5, c3-e5, f6-d4, a1-c3-e5, d6-f6-d4

To discipher the move notation look here.

### This makes the puzzle too easy!

Try turning off the assistance! Or try the opposite approach. On the 21-hole board, make some outrageous jumps that look like a disaster (but still never clicking on a bomb or black X), then hit Solve and watch the program pull off a one peg finish.

### How does it identify dead ends?

This is done by storing a key set of "winning" board positions. For details, see this paper.

### Why add the truncated triangle boards?

You might think that there is nothing new in the truncated triangle boards, since they are a subset of the triangle boards. However some jumps are eliminated in the truncated boards, as well as the corner pegs themselves. On the 15-hole triangle board, it is impossible to start with a peg missing in the middle, and end with one peg in the middle. However, the same problem is solvable on the 12-hole truncated triangle board!

George Bell, October 2014